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| 1. |
A hemispherical bowl of internal |
| Answer» Let the height of water in the cylindrical vessel be h cm.Given Internal radius of hemispherical bowl (r1) = 9 cm,Internal radius of the cylindrical bowl (r2) = 6 cmAs the content of hemispherical bowl has been put into the cylindrical vessel.{tex}\\Rightarrow{/tex}\xa0Volume of hemispherical bowl = Volume of cylindrical bowl{tex}\\Rightarrow \\frac { 2 } { 3 } \\pi r _ { 1 } ^ { 3 } = \\pi r _ { 2 } ^ { 2 } h{/tex}{tex}\\Rightarrow h = \\frac { 2 } { 3 } \\times \\left( \\frac { r _ { 1 } ^ { 3 } } { r _ { 2 } ^ { 2 } } \\right){/tex}{tex}\\Rightarrow h = \\frac { 2 } { 3 } \\times \\left( \\frac { 9 ^ { 3 } } { 6 ^ { 2 } } \\right){/tex}{tex}\\Rightarrow h = \\frac { 2 } { 3 } \\times \\frac { 729 } { 36 }{/tex}{tex}\\Rightarrow{/tex}\xa0h = 13.5 cmThus, the height of the water in the cylindrical vessel is 13.5 cm. | |